Estimation of Heterogeneous Within-Herd Variance Components Using Empirical Bayes Methods: A Simulation Study

¹ Department of Dairy Science, University of Wisconsin, Madison 53706

Genetic evaluation using BLUP can accommodate heterogeneous variances if the necessary variance components are known; this may require estimation of variance components within each heterogeneous subclass. Properties of sire and residual variance estimates obtained by an empirical Bayes approach, which combines within-herd and prior estimates, were examined via simulation. Prior estimates were obtained using REML across herds, as if variances were homogeneous. Convergence was improved by incorporation of prior information such that variance component estimates could be obtained in within-herd situations for which a REML algorithm failed to converge. Accuracy of sire variance estimates was greatest when both within-herd and prior information were used, but improvement in accuracy of residual variance estimates associated with incorporation of prior information was minimal. Correlations between sires' standardized true transmitting abilities and PTA that used empirical Bayes variance estimates were larger than those obtained when heterogeneity was ignored. Proportions of sues selected, based on standardized PTA, from environments with differing genetic and residual variances became more uniform as the relative weight placed on within-herd data in variance estimation increased. Thus, useful variance component estimates can be obtained within individual herds by using empirical Bayes methods with across-herd estimates as prior information; this may allow prediction of breeding values that are less influenced by heterogeneous variances.

Key Words: heterogeneous variance • best linear unbiased predictor • empirical Bayes methods

Submitted on April 15, 1992
Accepted on June 11, 1992